In this paper we derive the power series expansions of four infinite products of the form
\[
∏
n
∈
S
1
(
1
−
x
n
)
∏
n
∈
S
2
(
1
+
x
n
)
,
\prod \limits _{n \in {S_1}} {(1 - {x^n})\;\prod \limits _{n \in {S_2}} {(1 + {x^n}),} }
\]
where the index sets
S
1
{S_1}
and
S
2
{S_2}
are specified with respect to a modulus (Theorems 1, 3, and 4). We also establish a useful formula for expanding the product of two Jacobi triple products (Theorem 2). Finally, we give nonexistence results for identities of two forms.